Answer:
y = [tex]\frac{-7x}{2}+\frac{41}{2}[/tex]
Step-by-step explanation:
We are given the point (3, 10).
The second point is 2 on the x-axis and -7 on the y-axis. So our second point is: (3 + 2, 10 - 7) which is (5, 3).
Our formula for slope is m = [tex]\frac{rise}{run}[/tex] = [tex]\frac{y2-y1}{x2-x1}[/tex]
So, our equation would be [tex]\frac{3-10}{5-3}[/tex] = [tex]\frac{-7}{2}[/tex]
Using the standard formula of a line, y = mx + b, we can substitute for the slope, m.
y = [tex]\frac{-7x}{2}[/tex] + b
Now, we can substitute a point on the line to determine the y-intercept:
Using the point (3, 10),
10 = [tex]\frac{-7(3)}{2}[/tex] + b
b = 10 + [tex]\frac{21}{2}[/tex]
b = [tex]\frac{41}{2}[/tex]
So our full equation is: y = [tex]\frac{-7x}{2}+\frac{41}{2}[/tex]
